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lfunc_lfunctions • Show schema
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{'Lhash': 'dirichlet_L_927.130', 'a10': [-0.7390089172206591, -0.6736956436465572], 'a2': [0.3323547994796597, -0.9431544344712774], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [-0.7790805745256705, -0.6269238058941065], 'a5': [0.3897858732926794, -0.9209055179449537], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [0.8810121942857845, -0.47309355683601007], 'a8': [-0.8502171357296141, 0.5264321628773558], 'a9': [1.0, -2.8163065144692913e-30], 'algebraic': True, 'analytic_conductor': 99.6199852846174, 'analytic_normalization': 0, 'bad_lfactors': [[3, [1]], [103, [1]]], 'bad_primes': [3, 103], 'central_character': '927.130', 'coeff_info': ['x^102 - 1', '0.998103328737044 + 0.0615609061339428*I', '\\\\zeta_{102}'], 'conductor': 927, 'conductor_radical': 309, 'conjugate': 'dirichlet_L_927.763', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^82', 0, 'a^62', 'a^83', 0, 'a^94', 'a^42', 0, 'a^63', 'a^31', 0, 'a^26', 'a^74', 0, 'a^22', 'a^30', 0, 'a^78', 'a^43', 0, 'a^11', 'a^20', 0, 'a^64', 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[[1, '1.11469985404286145182078468259-0.823725947463664700836946767872*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.71316454108', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '1.67677987786', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.28649372177', 'prec': 44}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 99.6199852846174, 'bad_primes': [3, 103], 'central_character': '927.130', 'conductor': 927, 'conductor_radical': 309, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/927/130'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': False, 'is_instance_DIR': True, 'is_instance_ECNF': False, 'is_instance_ECQ': False, 'is_instance_G2Q': False, 'is_instance_HMF': False, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '1-927-927.130-r1-0-0', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [1], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'prelabel': '1-927-927.130-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 99.6199852846174, 'root_angle': -0.3034693538580219, 'self_dual': False, 'spectral_label': 'r1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.71316454108', 'prec': 44}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_927.130', 'Lhash_array': ['dirichlet_L_927.130'], 'label': '1-927-927.130-r1-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/927/130'}